Math  /  Numbers & Operations

Question(Author, Title, Pages) Example: The Bus Ride Taking the Dory Jagna Transit costs P 15.00 for the first ten kilometers (10 km)(10 \mathrm{~km}). Each additional ten kilometers adds P5.00P 5.00 to the fare. Moreover, if the trip reaches forty kilometers, the additional rate becomes P10.00P 10.00 for each ten-kilometer additional distance. Note that the vehicle's route is from Jagna to Tagbilaran (vice versa) only.
How much will a passenger pay for: a) a 5-kilometer ride? b) a 30-kilometer ride? c) a 60-kilometer ride?
Solution: a) For a 5-km ride: Since P15.00P 15.00 is the minimum fare, then for a minimum distance of 10 km , therefore a passenger will pay P15.00P 15.00. b) For a 30km30-\mathrm{km} ride: Since 30 km is beyond the minimum distance, and since the additional rate becomes P5.00P 5.00 per ten kilometers, we then have,
Fare == minimum fare + additional fare We must solve for the "additional fare" first:  Additional Fare = additional rate ×( distance travelled  min.  distance ) Additional Fare =(P5.0010 km/h)×(3010)km=P10.00\begin{array}{l} \text { Additional Fare }=\text { additional rate } \times(\text { distance travelled }- \text { min. } \text { distance }) \\ \text { Additional Fare }=\left(\frac{\mathbf{P} 5.00}{10 \mathrm{~km} / \mathrm{h}}\right) \times(30-10) \mathrm{km}=\mathrm{P} 10.00 \end{array}
Therefore, we get,  Fare =P15+P10=P25.00\text { Fare }=\mathbf{P} 15+\mathbf{P} 10=\mathbf{P} \underline{25.00} Exercises: 1) Solve for item c in the example. (Hint: Solve first for the "new minimum fare" at the distance of 40 km , which is now the "new minimum distance" to be considered.) 2) If you are the passenger en route to Tagbilaran City (roughly 69.79 km . away from Jagna), how much will you pay for the fare? (Note: Think practical.)

Studdy Solution

STEP 1

1. The fare structure is such that the first 10 kilometers cost P 15.00.
2. For distances greater than 10 kilometers but less than 40 kilometers, each additional 10 kilometers costs P 5.00.
3. For distances greater than or equal to 40 kilometers, each additional 10 kilometers costs P 10.00.

STEP 2

1. Calculate the fare for a 5-kilometer ride.
2. Calculate the fare for a 30-kilometer ride.
3. Calculate the fare for a 60-kilometer ride.

STEP 3

Calculate the fare for a 5-kilometer ride.
Since the distance is less than 10 kilometers, the fare is simply the minimum fare.
Fare=P15.00 \text{Fare} = P 15.00

STEP 4

Calculate the fare for a 30-kilometer ride.
The first 10 kilometers cost P 15.00. The remaining distance is 30 km - 10 km = 20 km. Each additional 10 kilometers costs P 5.00.
Additional Fare=(P5.0010 km)×20 km=P10.00 \text{Additional Fare} = \left(\frac{P 5.00}{10 \text{ km}}\right) \times 20 \text{ km} = P 10.00
So, the total fare is:
Fare=P15.00+P10.00=P25.00 \text{Fare} = P 15.00 + P 10.00 = P 25.00

STEP 5

Calculate the fare for a 60-kilometer ride.
The first 10 kilometers cost P 15.00. The next 30 kilometers (from 10 km to 40 km) cost P 5.00 per 10 kilometers.
Additional Fare (10 km to 40 km)=(P5.0010 km)×30 km=P15.00 \text{Additional Fare (10 km to 40 km)} = \left(\frac{P 5.00}{10 \text{ km}}\right) \times 30 \text{ km} = P 15.00
The remaining distance is 60 km - 40 km = 20 km. Each additional 10 kilometers beyond 40 kilometers costs P 10.00.
Additional Fare (40 km to 60 km)=(P10.0010 km)×20 km=P20.00 \text{Additional Fare (40 km to 60 km)} = \left(\frac{P 10.00}{10 \text{ km}}\right) \times 20 \text{ km} = P 20.00
So, the total fare is:
Fare=P15.00+P15.00+P20.00=P50.00 \text{Fare} = P 15.00 + P 15.00 + P 20.00 = P 50.00
Solution: - For a 5-kilometer ride, the fare is P 15.00. - For a 30-kilometer ride, the fare is P 25.00. - For a 60-kilometer ride, the fare is P 50.00.

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